Pixel-based partially coherent image method for maskless lithography system

Maskless lithography (ML) provides a fast and low-cost method for projecting the images of IC or micro features onto photoresist. However, it needs an efficient simulation method to evaluate the performance of lithography process. In this paper, a pixel-based partially coherent image method for digital micro-mirror device (DMD) based ML is proposed based on the linear invariant theory. In our method, the mask is sampled by DMD pixel (each pixel corresponding to each micro-mirror) and expressed by rect function. Using the shift theory of Fourier transform and the stacked pupil operator approach, we build a matrix Φ for system response function of rect function. If the DMD pixel state matrix is S, then the aerial image can be calculated with two matrix multiplication I(x,y) = SΦ.     

Study on the changes of ultrasonic parameters over supercritical Ni-Co electroplating process

This work discusses the influence of changes to ultrasound (US) parameters over the nickel cobalt (Ni-Co) metal thin film properties produced by supercritical CO₂ (SC-CO₂) electroplating. Additionally, Ni-Co films were produced by conventional electroplating and silent SC-CO₂ and compared against each other.The discussion on metal thin film properties revolves around variations to the bath type ultrasonic power (15 W and 20 W) and frequency (42 k Hz and 72 kHz) during experiments. The properties provided by the three electroplating processes and analyzed include: grain sizes, film elemental content analyses, surface microstructures, film hardness, corrosion resistance, surface roughness, crystalline structure and preferential growth, etc. From the results it was clear that quality of films produced by US-SC-CO₂ was improved compared to that of films produced by silent SC-CO₂, which itself was better than those produced by conventional electroplating. However, when US power was varied we observed a decline in the mechanical properties of the produced films.The combination of ultrasonic agitation with SC-CO₂ allows for improved mechanical properties such as: lower surface roughness, finer grain size and surface morphologies, increased corrosion resistance and film hardness. The ultrasound agitation applied to SC-CO₂ electroplating enhanced the formation of alloyed metal as ultrasonic agitation increased the electrolyte flowability during electroplating process resulting in increased mass transfer while at the same time achieving a surface cleaning effect which removed metal ions with poor adhesion and other unwanted particles. Moreover, application of ultrasonic agitation avoids the use of surfactants so only changes to the physical phenomena and no changes to the chemical composition of the deposited thin films were observed, meaning less pollution to the electrolyte and higher purity of the deposited films.The US-SC-CO₂ electroplating method described in this work effectively enhanced the mechanical properties of the deposited thin films compared to those produced by both silent SC-CO₂ and conventional electroplating processes.     

Bent函数的一般构造法

本文用概率方法给出小项表示的布尔函数谱的性质,据此得到了Ｂｅｎｔ函数的特征矩阵的等价刻画,原则上给出了Ｂｅｎｔ函数的一般构造法,并为Ｂｅｎｔ函数的计数问题提供了一个模型。文中还提出了Ｂｅｎｔ矩阵的概念,考察了Ｂｅｎｔ矩阵的性质,并借助Ｂｅｎｔ矩阵得到由已知Ｂｅｎｔ函数构造新的Ｂｅｎｔ函数构造新的Ｂｅｎｔ函数的方法。     

氢分子间色散相互作用能的自然轨道泛函

理论上对分子间色散相互作用能的精确计算一直是个难点问题.密度矩阵泛函基于非定域量一阶密度矩阵为基本变量,它与色散相互作用起源于电子间的非定域关联特性相吻合.论文以最简单的氢分子为研究对象,通过分析两相互平行的氢分子间色散相互作用能,构造出了该体系中色散相互作用能的自然轨道泛函.结果表明:描述该体系中色散相互作用能的自然轨道泛函形式为包含有4个轨道的非交换和库伦积分.该结果对发展色散相互作用能的密度矩阵泛函理论具有重要的参考价值.     

Darboux transformation and exact multisolitons for a matrix coupled dispersionless system

We present a matrix coupled dispersionless(CD) system. A Lax pair for the matrix CD system is proposed and Darboux transformation is constructed on the solutions of the matrix CD system and the associated Lax pair. We express an N soliton formula for the solutions of the matrix CD system in terms of quasideterminants. By using properties of the quasideterminants, we obtain some exact solutions, including bright and dark-type solitons, rogue wave and breather solutions of the matrix CD system. Furthermore, it has been shown that the solutions of the matrix CD system are expressed in terms of solutions to the usual CD system, sine-Gordon equation and Maxwell-Bloch system.     

A rational Arnoldi approach for ill-conditioned linear systems

For the solution of full-rank ill-posed linear systems a new approach based on the Arnoldi algorithm is presented. Working with regularized systems, the method theoretically reconstructs the true solution by means of the computation of a suitable function of matrix. In this sense, the method can be referred to as an iterative refinement process. Numerical experiments arising from integral equations and interpolation theory are presented. Finally, the method is extended to work in connection with the standard Tikhonov regularization with the right-hand side contaminated by noise.     

基于乘性模糊互补判断矩阵的FAHP

根据乘性一致性的定义,从人的主观判断与其权重的函数关系出发,获得了乘性模糊互补判断矩阵的元素表达式,论证了利用乘性模糊互补判断矩阵求取因素相对权重的可行性,最后给出了一种基于乘性一致模糊判断矩阵的排序方法.从而使得乘性模糊互补判断矩阵的应用的理论基础更加坚实.     

微波消解ICP-AES法同时测定花岗石中铜、镉、铬和砷

本文采用微波消解和ICP－AES法，同时测定花岗石样品的铅、镉、铬、砷4有害元素，检出限分别为0．0008、0．0007、0．0018、0．0012μg.mL^-1,回收率为93．4％－102．5％，RSD为1．3％－3．6％，该法准确、快速、简便，结果令人满意。     

The Constrained Solutions of Two Matrix Equations

We study the symmetric positive semidefinite solution of the matrix equation AX ₁ A ^T + BX ₂ B ^T = C, where A is a given real m×n matrix, B is a given real m×p matrix, and C is a given real m×m matric, with m, n, p positive integers; and the bisymmetric positive semidefinite solution of the matrix equation D ^T XD = C, where D is a given real n×m matrix, C is a given real m×m matrix, with m, n positive integers. By making use of the generalized singular value decomposition, we derive general analytic formulae, and present necessary and sufficient conditions for guaranteeing the existence of these solutions. Received December 17, 1999, Revised January 10, 2001, Accepted March 5, 2001